# Conversions between the common units of length used in the Imperial system are listed below 12 in = 1 ft 3 ft = 1 yard 1760 yards = 1 mile

Save this PDF as:

Size: px
Start display at page:

Download "Conversions between the common units of length used in the Imperial system are listed below 12 in = 1 ft 3 ft = 1 yard 1760 yards = 1 mile"

## Transcription

1 THE METRIC SYSTEM The metric system or SI (International System) is the most common system of measurements in the world, and the easiest to use. The base units for the metric system are the units of: length, measured in meters (m); time, measured in seconds (s); mass, measured in grams (g); and temperature, measured in Celsius ( C). In the metric system, prefixes are used to describe multiples or fractions of the base units. The most common metric system prefixes are: nano (n)... / 100,000,000 micro (µ)... / 1,000,000 milli (m)... / 1,000 centi, (c)... / 100 deci (d)... / 10 deca (da)...x 10 hecto (h)...x 100 kilo (k)...x 1,000 mega (M)...x 1,000,000 giga (G)...x 1,000,000,000 Using the base unit for length: 1 nanometer (nm) = 1 m / 100,000,000 = m 1 micrometer (µm) = 1 m / 1,000,000 = m 1 millimeter (mm) = 1 m / 1,000 = m 1 centimeter (cm) = 1 m / 100 = 0.01 m 1 decimeter (dm) = 1 m / 10 = 0.1 m 1 decameter (dam) = 1 m x 10 = 10 m 1 hectometer (hm) = 1 m x 100 = 100 m 1 kilometer (km) = 1 m x 1,000 = 1,000 m 1 megameter (Mm) = 1 m x 1,000,000 = 1,000,000 m 1 gigameter (Gm) = 1 m x 1,000,000,000 = 1,000,000,000 m Similarly for mass, you will often see the following units: 1 milligram (mg) = 1 g / 1,000 = g 1 kilogram (kg) = 1 g x 1,000 = 1,000 g

2 2 THE IMPERIAL SYSTEM The Imperial system is more complicated than the metric system, as it does not work in multiples of 10 as the metric system does. The Imperial system is used in England and the United States, and you will probably recognize many of the units used. In the Imperial system the base units are: length, commonly measured in inches (in), feet (ft), yards and miles; time, commonly measured in seconds (s), hours (hr), days (d), weeks and years (yr); weight, commonly measured pounds (lb); and temperature, measured in Fahrenheit ( F). Note that the Imperial system commonly uses weight, rather than mass. Weight refers to the gravitational pull on an object, whereas mass refers to the amount of matter in the object. An object would have the same mass on the moon as it does on the earth, but it would weight less on the moon as the gravitational pull of the moon is less than the gravitational pull of the earth. Astronauts have the same mass on the moon as they do on the earth, but they can jump higher on the moon because they weigh less there! This difference does not affect us much as all the problems we will be solving assume we are on the earth, but you should be aware of it. Conversions between the common units of length used in the Imperial system are listed below 12 in = 1 ft 3 ft = 1 yard 1760 yards = 1 mile The units of time are generally accepted for use with the metric system, as well as the Imperial system. Conversions between the common units of time are listed below: 60 s = 1 min 24 hrs = 1 day 7 days = 1 week 52 weeks = 1 yr Conversion between Metric and Imperial The tables on the next two pages give the conversions between Metric and Imperial. These tables come attached to the exam, and you should know how to use them. Math questions on the exam generally give both metric and imperial units, allowing you to work in whichever system you are most comfortable in. It helps if you can convert between the two systems to check your answers!

3 3 LENGTH N = number of sections L = length of section X = total length Units of Measurement: Metric (SI): mm = millimeters cm = centimeters m = meters km = kilometers Imperial: in. = inches ft = feet yards miles Conversion: Metric (SI): Metric to Imperial (and back): 1 cm = 10 mm 1 in = 2.54 cm cm x 10 = mm cm x = inches mm x 0.1 = cm inches x.54 = cm 1 m = 100 cm 1 ft = cm m x 100 = cm cm x = feet cm x 0.01 = m feet x = cm 1 m = mm 1 m = ft m x = mm m x = feet mm x = m feet x = m 1 km = m 1 mile = km km x = m km x = miles m x = km miles x = km

4 4 Length: Questions 1. If I have 7 sections of pipe, each 3.0 m long, what is the total length of line I can replace? Given: L = N = X = L x N Find: X = 2. If I have to replace 21 m of pipeline, and each pipe is 3.0 m long, how many sections of pipe will I need? Given: X = L = Find: N = N = X L 3. A line has failed and 23 m must be replaced. How many 3.0 m long section of pipe will be needed to repair the line? Given: X = L = Find: N = N = X L 4. A line has failed and 1.6 km must be replaced. How many 6 m long section of pipe will be needed to repair the line? Given: X = L = Find: N = N = X L 5. A line has failed and 0.7 km must be replaced. How many 3.5 m long section of pipe will be needed to repair the line? Given: X = X L = N = L Find: N =

5 5 Length: Discussion and Answers The first 5 questions on length are designed to introduce the concepts of basic problems solving, using and rearranging simple equations, identifying given parameters and calculating unknown parameters, knowing whether to round up or down, and converting between different units within the metric system. Question 1: Using Equations The basic equation is: X = L x N where: N = number of sections L = length of section X = total length In plain English the equation reads: The total length of the pipe equals the length of one section multiplied by the number of sections. IMPORTANT: The student should always remember to note units! 1. If I have 7 sections of pipe, each 3.0 m long, what is the total length of line I can replace? Given: L = 3.0 m N = 7 (no units) Find: X Solution: X = L x N = 3.0 m x 7 = 21.0 m Question 2: Rearranging Equations 2. If I have to replace 21 m of pipeline, and each pipe is 3.0 m long, how many sections of pipe will I need? Given: X = 21 m L = 3.0 m Find: N As with the first question, the basic equation is: X = L x N In Question 2, we are given the total length (X) and the length of each section (L), and we have to find out how many sections we need (or solve for N).

6 6 When we rearrange an equation, we have to do the same thing to both sides to keep the equation equal. The first step in rearranging is to identify which parameter we have to solve for, and isolate that parameter on the left side. In this case we are solving for N, so we divide both sides of the equation by L. After rearranging, the equations becomes: X = L LxN L Since any number divided by itself equals one, L/L cancels out. Switching sides, the equation becomes: N = X L In plain English the equation reads: The number of sections required is equal to the total length of the pipe divided by the length of one section. Solution: N = X L 21m = 3.0m = 7 Question 3: Rounding 3. A line has failed and 23 m must be replaced. How many 3.0 m long section of pipe will be needed to repair the line? Given: X = 23 m L = 3.0 m Find: N The equation used in Questions 3 to 5 is the same as that used in Question 2, but here the answer does not come out to an even number. The operator should know that they need to round the answer up, otherwise they would not have enough pipe to replace the full length of the failed section. Solution: N = X L

7 7 23m = 3m =7.67m You will need eight sections of pipe to fix the line. Questions 4 and 5: Converting to Consistent Units 4. A line has failed and 1.6 km must be replaced. How many 6 m long section of pipe will be needed to repair the line? The operator should know they should always be working in the same or compatible units. Here, X is given in kilometers and L in meters. The operator must convert either X or L. Given: X = 1.6 km = 1,600 m L = 6 m Find: N Solution: X N = L 1,600m = 6m = You will need 267 sections of pipe to repair the line. 5. A line has failed and 0.7 km must be replaced. How many 3.5 m long section of pipe will be needed to repair the line? Given: X = 0.7 km = 700 m L = 3.5 m Find: N Solution: X N = L 700m = 3.5m = 200 You will need at least 200 sections of pipe to repair the line.

8 8 AREA W = width L = length Units of Measurement: Metric (SI): m 2 = square meters ha = hectares Imperial: ft 2 = square feet = ft. sq. square yards acres Conversion: Metric (SI): Metric to Imperial (and back): 1 m 2 = cm 2 1 m 2 = square feet m 2 x = cm 2 m 2 x = square feet cm 2 x = m 2 feet square x = m 2 1 ha = m 2 1 ha = acres ha x = m 2 ha x = acres m 2 x = m 2 acres x = ha

9 9 Area of a Rectangle: Questions W = 3 m L = 4 m 1. A floor measures 4 m by 3 m. What is the area of the floor? Given: L = W = A = L x W Find: A = 2. A floor has a length of 4 m and an area of 12 m 2, what is the width of the floor? Given: A = A L = W = L Find: W = 3. A floor has a width of 3 m and an area of 12 m 2, what is the length of the floor? Given: A = A W = L = W Find: L =

10 10 Area of a Rectangle: Questions W = 2.3 m L = 3.7 m 4. A floor measures 3.7 m by 2.3 m. What is the area of the floor? Given: L = W = Find: A = 5. A floor has a length of 3.7 m and an area of 8.5 m 2, what is the width of the floor? Given: A = L = Find: W = 6. A floor has a width of 2.3 m and an area of 8.5 m 2, what is the length of the floor? Given: A = W = Find: L =

11 11 Area of a Rectangle: Discussion The basic equation for calculating the area of a square or rectangle is: A = L x W In plain English the equation reads: The area of a rectangle is equal to the length times the width, or the area of a rectangle is equal to the length multiplied by the width. Note that a square is simple the special case of a rectangle where the length is equal to the width. The more general term rectangle is therefore used in the discussion. The questions relating to area of a rectangle reinforce the concepts of basic problems solving, identifying given parameters and calculating unknown parameters and using and rearranging simple equations. The student should clearly understand the meaning of the unit m 2 (meters square), in the sense that: 1 m 2 = 1 m x 1 m = 1 m x m Similarly, the units square inch or square feet, where: 1 sq. in. = 1 in 2 = 1 in x 1 in = 1 in x in 1 sq. ft. = 1 ft 2 = 1 ft x 1 ft = 1 ft x ft In addition, the student should be familiar with different formats for expressing multiplication. Note that the equation: A = L x W can also be written in the following ways: A = (L)(W) A = LW A = L W A = L * W

12 12 Area of a Rectangle: Answers 1. A floor measures 4 m by 3 m. What is the area of the floor? Given: L = 4 m W = 3 m Find: A Solution: A = L x W = 4 m x 3 m = 12 m x m = 12 m 2 2. A floor has a length of 4 m and an area of 12 m 2, what is the width of the floor? Given: A = 12 m 2 Find: Solution: L W W = = 4 m A L 12mxm = 4m =3 m 3. A floor has a width of 3 m and an area of 12 m 2, what is the length of the floor? Given: A = 12 m 2 Find Solution: W = 3 m L A L = W 12mxm = 3m = 4 m Questions 4 to 6 are similar but the student should be comfortable working with decimal places and should know when to round up and when to round down. 4. A = 8.5 m 2 5. W = 2.3m 6. W = 3.7m

13 13 Area of a Circle: Questions R = radius A = π R 2 D R = 2 D= diameter D = 2 x R 1. A circle has a radius of 3 m. What is the area of the circle? Given: R = Find: A = 2. A circle has a diameter of 6 m. What is the area of the circle? Given: D= Find: R = A = 3. A circle has a radius of 3.8 m. What is the area of the circle? Given: R = Find: A =

14 14 Area of a Circle: Discussion The water treatment plant operator often works with circular containers, and must be able to calculate the area and volume of these containers. This section introduces the formula used to calculate the area of a circle, and the concepts of Pi (π) and radius squared (R 2 ). The radius of a circle is the length from the centre of the circle to the edge of the circle. The units of radius (R) are the units of length. The term R 2 means: R 2 = R x R The units of R 2 will be a unit of length squared such as m 2, in 2 or ft 2 : Pi (π) is a number that relates the radius of a circle to its area. Pi is always equal to: π = This is typically rounded to: π = 3.14 The basic formula for calculating the area of a circle is: A = π R 2 In plain English the equation reads: The area of a circle is equal to Pi(3.14) times the radius squared. The diameter of a circle (D) is the length from one side of a circle to the other. Diameter (D) is equal to twice the radius, or: D = 2 R Similarly, by rearranging the equation, we know the radius is equal to half the diameter, or D R = 2 If a question gives the diameter of the circle, the student should calculate the radius first and then the area.

15 15 Area of a Circle: Answers 1. A circle has a radius of 3 m. What is the area of the circle? Given: R = 3 m Find: A Answer: A = π R 2 = 3.14 (3 m)(3 m) = (m)(m) = 28.3 m 2 2. A circle has a diameter of 6 m. What is the area of the circle? Given: D = 6 m Find: A D Answer: R = 2 6m = 2 = 3 m A = π R 2 = (3.14)(3 m)(3 m) = 28.3 m 2 3. A circle has a radius of 3.8 m. What is the area of the circle? Given: R = 3.8 m Find: A Answer: A = π R 2 = 3.14 (3.8 m)(3.8 m) = 45.3 m 2 VOLUME

16 16 H = height L= length W = width Units of Measurement: Metric (SI): cm 3 = cubic centimeters m 3 = cubic meters = cu m L = liters ml = milliliters Imperial: ft 3 = cubic feet = ft. cu. gallons (Imperial) = Imp. gal. = ig US gallons Conversion: Metric (SI): Metric to Imperial (and back): 1 m 3 = cm 3 1 m 3 = cubic feet m 3 x = cm 3 m 3 x = cubic feet cm 3 x = m 3 cubic feet x = m 3 1 m 3 = L 1 gallon (Imperial) = L m 3 x = L l x = gallons (Imperial) l x = m 3 gallons (Imperial) x = L 1 l = ml 1 gallon (Imperial) = US gallons L x = ml US gallons x = Imperial gallons m x = L Imperial gallons x = US gallons 1 ml = 1 cm 3 ml x 1 = cm 3 cm 3 x 1 = ml

17 17 Volume of a Box: Questions H = 7 cm L= 24 cm W = 12 cm 1. A box has a top area of 1.92 m 2 and a height of 1.2 m. What is the volume of the box? 2. A box of has a length of 24 cm, a width of 12 cm and a height of 7 cm. What is the area of the top of the box and the volume of the box? 3. A box of has a length of 1.6 m, a width of 92 cm and a height of 1.2m. What is the volume of the box in cm 3, m 3 and L? 4. A Foreman places 3 m 3 of sand in a container 2.4 m long and 1.8 m wide. What is the height of sand in the container? 5. A Foreman places 60 L of water in a container 2.4 m long and 1.8 m wide. What is the height of water in the container? 6. A water tank 2.4 m long and 1.8 m wide has 1.2 m of water in it in the morning. By the end of the day, the container has 1.7 m of water in it. How much water was added to the container that day? 7. A water tank 2.4 m long and 1.8 m wide has 1.2 m of water in it in the morning. If we add another 850 L of water to the tank, what will be the height of water in the tank? Volume of a Box: Discussion

18 18 By now, the student should be familiar with the basic problem solving technique: identifying what is given, what they need to find, what equation to use, whether they need to rearrange the equation, and substituting the given values into the equation to find the required value. The basic equation for calculating volume, is area of the top or base times the height. In the case of a box, the area of the top or base is equal to the length times the width: V= A x H where H = height A = L x W Substituting the equation for area into the equation for volume, we get: or: V = (L x W) x H V= L x W x H In plain English the equation reads: The volume of a box is equal to the length times the width times the height. The student should understand the meaning of the unit m 3 (cubic meters), in the sense that: 1 m 3 = 1 m x 1 m x 1 m= 1 m x m x m Similarly, the units cubic inch or cubic feet, where: 1 cu. in. = 1 in 3 = 1 in x 1 in x 1 in = 1 in x in x in 1 cu. ft. = 1 ft 3 = 1 ft x 1 ft = 1 ft x ft x ft In the metric system, volume, particularly liquid volume, is often measured in L or ml. Keep in mind that: 1 l = 1 dm3 = 1 dm x 1 dm x 1 dm 1 ml = 1 cm 3 = 1 cm x 1 cm x 1 cm 1 m 3 = 1,000 L 1 L = 1,000 ml Volume of a Box: Answers

19 19 1. A box has a top area of 1.92 m 2 and a height of 1.2 m. What is the volume of the box? Given: A = 1.92 m 2 Find: Solution: H = 1.2 m V V = A x H = (1.92 m 2 )(1.2 m) = (m x m)(m) = 2.3 m 3 2. A box of has a length of 24 cm, a width of 12 cm and a height of 7 cm. What is the area of the top of the box and the volume of the box? Given: L = 24 cm W = 12 cm H = 7 cm Find: A and V Solution: A = L x W = (24 cm)(12 cm) =288 cm 2 V = A x H = (288cm 2 )(7 cm) = 2016 cm 3 3. A box of has a length of 1.6 m, a width of 92 cm and a height of 1.2m. What is the volume of the box in cm 3, m 3 and L? Given: L = 1.6 m W = 92 cm H = 1.2 m Find: Solution: V in cm 3, m 3 and L V = L x W x H First convert all given parameters to consistent units. In this case you can convert to either cm or m. If we convert to m: cm x 0.01 = m W = 92 cm x 0.01 = 0.92 m V = L x W x H = (1.6 m)(0.92 m)(1.2 m) = 1.77 m 3

20 20 m 3 x = cm 3 V = 1.77 m 3 x = 1,770,000 cm 3 m 3 x = L V = 1.77 m 3 x = 1,770 L 4. A Foreman places 3 m 2 of sand in a container 2.4 m long and 1.8 m wide. What is the height of sand in the container? Given: V = 3 m 2 Find: Solution: L = 2.4 m W = 1.8 m H W = L x W x H To isolate H, we divide both sides of the equation by L x W V LxW xh = LxW LxW LxW V = 1, therefore = 1H, or LxW LxW V H = LxW = 3 3 m (2.4m)(1.8 = 0.69 m m) 5. A Foreman places 60 l of water in a container 2.4 m long and 1.8 m wide. What is the height of water in the container? Given: V = 60 L L = 2.4 m W = 1.8 m Find: H Solution: First convert all parameters to consistent units, in this case m, L x = m 3 V = 60 L x = 0.06 m 3 H = V LxW m = (2.4m)(1.8m) = m

21 21 m x 100 = cm H = m x 100 = 1.4 cm 6. A water tank 2.4 m long and 1.8 m wide has 1.2 m of water in it in the morning. By the end of the day, the container has 1.7 m of water in it. How much water was added to the container that day? Given: L = 2.4 m W = 1.8 m H 1 = 1.2 m H 2 = 1.7 m Find: Solution: V Note all measurements are given in m, so we do not have to convert. In this case we are interested only in the volume of water added to the tank, so the height we need is the difference between the height of water in the tank in the morning and the height of water in the tank in the evening. H = H 2 H 1 = 1.7 m 1.2 m = 0.5 m V = L x W x H = (2.4 m)(1.8 m)(0.5 m) = 4.82 m 3 m 3 x = L V = 4.82 m 3 x 1,000 = 4820 L 7. A water tank 2.4 m long and 1.8 m wide has 1.2 m of water in it in the morning. If we add another 850 l of water to the tank, what will be the height of water in the tank? Given: L = 2.4 m W = 1.8 m H 1 = 1.2 m V = 850 L Find: H 2 Solution: First convert all parameters to consistent units: L x = m 3 V = 850 l x = 0.85 m 3 H = V LxW

22 m = (2.4m)(1.8m) = 0.20 m In this case H is the difference between the height of water in the tank in the morning, and the height of water in the tank after adding another 850 l. To find the total height of water in the tank after adding 850 l, we have to add the original height to height difference, or: H 2 = H 1 + H = 1.2 m m = 1.4 m

23 23 Volume of a Cylinder: Questions R = radius D = diameter H = height 1. An upright cylindrical drum has a radius of 3 m and a height of 2 m. What is the area of the lid and the volume of the cylinder in m 3? 2. a) An upright cylinder has a diameter of 0.5 m and a height of 2.6 m. What is the volume of the cylinder in m 3 and L? b) The cylinder from question 2a is filled with water to a depth of 1.8 m. How much water is in the cylinder? 3. An upright cylindrical tank with a diameter of 3 m, was filled to a depth of 2.3 m in the morning and 1.5 m at the end of the day. Assuming there was no water added to the tank that day, how much water was taken out? 4. A water treatment plant operator has a chlorine mixing tank with a diameter of 0.8 m, and a depth of 1.1 m. If there is 0.2 m of chlorine solution left in the tank, and the operator decides not to empty the tank before adding an addition 150 L of water, what will be the depth of liquid in the tank after adding the extra water? 5. How many litres of water can be held in 15 m of 200 mm pipe?

24 24 Volume of a Cylinder: Answers Questions 1 to 4: Cylindrical Tanks 1. An upright cylindrical drum has a radius of 3 m and a height of 2 m. What is the area of the lid and the volume of the cylinder in m 3? Given: R =3 m H = 2 m Find: A and V Solution: A = π R 2 = (3.14)(3 m) 2 = (3.14)(3 m)(3 m) = 28.3 m 2 V = A x H = (28.26 m 2 )(2 m) = 56.5 m 3 2. a) An upright cylinder has a diameter of 0.5 m and a height of 2.6 m. What is the volume of the cylinder in m 3 and l? Given: D = 0.5 m H = 2.6 m Find: Solution V in m 3 and L D R = 2 0.5m = 2 = 0.25 m V = A x H = π R 2 H = (3.14)(0.25 m)(0.25 m)(2.6 m) = 0.51 m 3 m 3 x = L V = 0.51 m 3 x = 510 L

25 25 2. b) The cylinder from question 2a is filled with water to a depth of 1.8 m. How much water is in the cylinder? Given: D = 0.5 m R = 0.25 m (calculated above) H = 1.8 m Find: Solution V in m 3 and L V = π R 2 H = (3.14)(0.25 m)(0.25 m)(1.8 m) = 0.35 m 3 m 3 x = L V = 0.35 m 3 x = 350 L 3. An upright cylindrical tank with a diameter of 3 m, was filled to a depth of 2.3 m in the morning and 1.5 m at the end of the day. Assuming there was no water added to the tank that day, how much water was taken out? Given: D = 3 m H 1 = 2.3 m H 2 = 1.5 m Find: Solution V D R = 2 3m = 2 = 1.5 m H = H 1 H 2 = 2.3 m 1.5 m = 0.8 m V = π R 2 H = (3.14)(1.5 m)(1.5 m)(0.8 m) = 5.65 m 3 m 3 x = L V = 5.65 m 3 x 1,000 = 5,650 L

26 26 4. A water treatment plant operator has a chlorine mixing tank with a diameter of 0.8 m, and a depth of 1.1 m. If there is 0.2 m of chlorine solution left in the tank, and the operator decides not to empty the tank before adding an addition 150 L of water, what will be the depth of liquid in the tank after adding the extra water? Given: D = 0.8 m H 1 = 0.2 m V = 150 L Find: H 2 Solution D R = 2 0.8m = 2 =0.4 m The basic equation is: V = π R 2 H Rearranging for H, where H is the extra height of the water added H V = π R 2 Converting V to get consistent units, L x = m 3 V = 150 l x = 0.15 m m H = (3.14)(0.4m)(0.4m) = 0.3 m The total depth of water in the tank will be equal to the initial depth of water plus the height of the water added. H 2 = H 1 + H = 0.2 m m = 0.5 m

27 27 Questions 5: Pipes Questions relating to pipes are similar to those relating to cylindrical tanks. The basic equation is the same, except that in this case H, refers to the length of the pipe. 5. How many litres of water can be held in 15 m of 200 mm pipe? Given: D =200 mm H =15 m Find: V in L Solution First we have to convert to consistent units, in this case, m: mm x = m D = 200 mm x = 0.2 m D R = 2 0.2m = 2 =0.1 m V = A x H = π R 2 H = (3.14)(0.1 m)(0.1 m)(15 m) = 0.47 m 3 m 3 x = L V = 0.47 m 3 x = 470 L

28 28 FLOW RATE Definition: The volume of liquid passing through a specific point over a given period of time. For example, the volume of water coming out the end of a tap in one minute or the volume of water passing through a pump in a day or an hour, or the volume of water pumped through a water treatment plant in a year, a month or a week. V Q = T T = Time Q = Flowrate V = Volume Units of Measurement: Metric (SI): L/s = litres per second L/min = litres per minute L/hr = litres per hour m 3 /s = meters cubed per second m 3 /day = meters cubed per day ML/day = million litres per day ML/yr = million litres per year Imperial: ft 3 /s = cubic feet per second GPM (Imp.) = gallons (Imperial) per minute US GPM= gallons (US) per minute ig/min = gallons (Imperial) per minute ig/d = gallons (Imperial) per day Conversion: Metric (SI): Metric to Imperial (and back): 1 L/min = 60 L/s 1 gallon (Imperial)/min = L/min L/min x 60 = L/s L/min x = gallons (Imp.) per minute L/s x = L/min gallons (Imp.) per minute x = L/min 1 L/day = 24 L/hr 1 gallon per day = L/d L/day x 24 = L/hr L/d x = gallons (Imp.) per day L/hr x = L/day gallons (Imp.) per day x = L/d 1 m 3 /day = L/day 1 m 3 /s = cubic feet per second m 3 /day x = L/day m 3 /s x = cubic feet per second L/day x = m 3 /day cubic feet per second x = m 3 /s

29 29 Flowrate: Questions 1. It takes 3 min to fill An 12 L jar. What is the flowrate of the water? 2. Water is flowing at a rate of 4 L/min and it takes 3 min to fill a jar. How big is the jar? 3. At a flowrate of 4 L/min, how long does it take to fill a 12 L jar? 4. Water is flowing at a rate of 3.7 L/min and it takes 2.3 min to fill a jar. How big is the jar? 5. It takes 2.3 min to fill An 8.5 L jar. What is the flowrate of the water? 6. At a flowrate of 3.7 L/min, how long does it take to fill an 8.5 L jar? 7. A total of 3,105 m 3 passes through a flow meter in 3 days. What is the flowrate in m 3 /day and l/day? 8. A flowmeter reads l on Monday morning and l on Thursday morning the same week. What is the average daily flow? 9. At a flow rate of 1,000 l/min, how many days would it take to fill a reservoir that 50 m long, 20 m wide and 2 m deep? 10. At a flow rate of 16 m 3 /hr, how long would it take to fill an upright cylindrical tank with a diameter of 5 m and a height of 3.6 m?

30 30 Flowrate: Answers 1. It takes 3 min to fill An 12 l jar. What is the flowrate of the water? Given: Find: Solution: V = 12 l T = 3 min Q V Q = T 12l = 3 min = 4 L/min 2. Water is flowing at a rate of 4 L/min and it takes 3 min to fill a jar. How big is the jar? Given: Q = 4 L/min Find: Solution: T = 3 min V The basic equation is: V Q = T Multiply both sides of the equation by T to isolate V, V = Q x T = 4 L/min x 3 min = 12 L 3. At a flowrate of 4 L/min, how long does it take to fill a 12 L jar? Given: Q = 4 L/min Find: V = 12 L T Solution: Multiply both sides of the basic equation by Q T to isolate T, V T = Q 12L = 4L / min = 3 min 4. Water is flowing at a rate of 3.7 L/min and it takes 2.3 min to fill a jar. How big is the jar?

31 31 Given: Find: Solution: Q = 3.7 L/min T = 2.3 min V V = Q x T = (3.7 L/min)(2.3 min) = 8.5 L 5. It takes 2.3 min to fill An 8.5 L jar. What is the flowrate of the water? Given: V = 8.5 L Find: Solution: T = 2.3 min Q V Q = T 8.5L = 2.3 min = 3.7 l/min 6. At a flowrate of 3.7 L/min, how long does it take to fill an 8.5 L jar? Given: Q = 3.7 l/min Find: Solution: V = 8.5 l T V T = Q 8.5L = 3.7L / min = 2.3 min 7. A total of 3,105 m 3 passes through a flow meter in 3 days. What is the flowrate in m 3 /day and L/day? Given: V =3,105 m 3 Find: Solution: T = 3 days Q V Q = T

32 32 3,105m = 3days 3 = 1,035 m 3 /day m 3 /day x = L/day Q = 1,035 m 3 /day x = 10,035,000 L/day 8. A flowmeter reads L on Monday morning and L on Thursday morning the same week. What is the average daily flow? Given: V 1 =134,567,030 L Find: Solution: V 2 = 137,672,428 L T 1 = Monday morning T 2 = Thursday morning Q V Q = T V = V 2 V 1 = 137,672,428 L - 134,567,030 L = 3,105,398 L T = T 2 T 1 = 3 days 3,105,398L Q = 3days = 1,035,000 L/day 9. At a flow rate of 1,000 l/min, how many days would it take to fill a reservoir that 50 m long, 20 m wide and 2 m deep? Given: Q = 1,000 l/min Find: Solution: L = 50 m W = 20 m D = 2 m T V T = Q V = L x W x H

33 33 = (50 m)(20 m)(2 m) = 2,000 m 3 m 3 x = L V = 2,000 m 3 x = 2,000,000 L 2,000,000L T = 1,000L / min = 2,000 min 1 day = 24 hrs = min min x 1day 1,440 min T = 2,000 min x = days 1day 1,440 min = 1.4 days 10. At a flow rate of 16 m 3 /hr, how long would it take to fill an upright cylindrical tank with a diameter of 5 m and a height of 3.6 m? Given: Q = 16 m 3 /hr D = 5 m H = 3.6 m Find: Solution: T V T = Q V = π R 2 H R = 2 D = 5m 2 = 2.5 m V = (3.14)(2.5 m)(2.5 m)(3.6 m) = m m = 3 16m / hr = 4.4 hrs

34 34 PRESSURE, FORCE AND HEAD Definitions: Force The push that is exerted by water, on the surface that is confining or containing it. Force can be expressed in pounds, tons, grams or kilograms. As an example, a certain volume of water may be exerting 22 pounds of force on the bottom of the bucket that is containing it. Pressure The amount of force per unit of area. Pressure is often measured in pounds per square inch (psi). It may also be expressed in kilopascals (kpa). 1 psi = 6.89 kpa It helps to remember that one cubic foot (1 foot 3 ) of water always weighs 62.4 pounds. A cubic foot of water also contains approximately 7.5 gallons (34L). To calculate the pressure of a cubic foot of water, we need to know that the area the force is being exerted upon is 12 X 12 inches (144 square inches). Therefore, 62.4 pounds per 144 inches can be converted to a pressure per square inch (psi). 1 cubic foot of water = 62.4 pounds 1 foot We can divide 62.4 by 144, and we will find that The pressure exerted is psi. 1 foot 1 foot This means that a column of water that is one square inch and one foot tall exerts a pressure of pounds: pound of pressure 1 foot

36 36 Pressure, Force and Head: Questions 1. Using the conversion factor that you learned for pressure, convert 2.8 psi to kpa. 2. Calculate the head for a volume of water which exerts 12 psi of pressure. 3. If there are two tanks (one holds 3000L and one holds 1800L) that are the same height, but have different diameters, which will have a greater reading on its pressure gauge if they are both full to the top? (see figure below) 1800L 3000L Pressure gauges

38 38 Chlorine Dosage /Feed Rate Definition: Dosage: Amount of chemical applied to water expressed in parts per million (PPM) or milligrams per litre (mg/l). Feed Rate: amount of chlorine added to treat a volume of water over a course of time. Residual: amount of active chlorine in water that can be free available chlorine which is uncombined and available to react water properties, combined which is chlorine combined primarily with organics and not very reactive and total residual is the amount of available chlorine and combined chlorine. Note: It is most important for a plant operator to know how to calculate the dosages of the various chemicals used in water treatment. It is important to be accurate when calculating dosages, as too little chemical may be ineffective and too much may waste money. Exact dosage must be determined through calculation for the purpose of efficient operation and economy. Chlorine Dose = C x 1000 W C D = Chlorine dose C = Chlorine feed rate in kg/day W = volume of water to be treated in m 3 Feed rate = W x CD Residual: Dosage - Demand = Residual 1000 Residual + Demand = Dosage Example: Dosage 3.7 mg/l Subtract Demand 3.0 mg/l Dosage: Calculations Equals Residual 0.7 mg/l 1. The chlorine dosage of an effluent is 15mg/L. How many kilograms of chlorine will be required to dose a flow of m 3 / d? 2. A chlorinator is set to feed a 94.8 kg/d of chlorine. If the average daily flow through the plant is m 3 / d, what is the DAILY AVERAGE CHLORINE DOSAGE IN mg/l? 3. Chlorine dosage is 2.5 mg/l and the Flow rate is m 3 /d, what is the feed rate? 4. What should be the chlorine dose of water that has a chlorine demand of 2.3 mg/l if a residual of 0.5 mg/l is desired?

39 39 HYPOCHLORINATION Hypochlorination is the application of hypochlorite ( a compound of chlorine and another chemical), usually in the form of a solution, for disinfection purposes. 5. The treated product at a water treatment plant requires a chlorine dosage of 98 kg/d for disinfection purposes. If we are using a solution of hypochlorite containing 60% available chlorine, how many kg/d hypochlorite will be required? 6. A hypochlorite solution contains 5% available chlorine. If 4 kg of available chlorine are needed to disinfect a water main, how much 5% solution would be required? BATCH CHLORINATION Batch chlorination is a method of disinfection where by the chlorine is added to a water tank manually. This type of chlorination is used when mechanical methods for chlorination are not available most commonly used to disinfect water in a water truck. C 1 V 1 = C 2 V 2 V 1 = C 2 V 2 C 1 C 1 = Concentration of liquid chlorine solution V 1 = Volume of liquid chlorine solution needed C 2 = Chlorine Dose in Truck V 2 = Volume of water Truck 7. How much liquid bleach (4.5 % chlorine solution) should you add to your 3800L water truck to achieve a chlorine concentration of 0.5 mg/l? 8. What is the concentration of the chlorine solution that was added to 5000L water truck with a chlorine concentration of 1.2 mg/l?

40 40 Dosage: Answers 1. In this question, it will be necessary to utilize your knowledge of the metric system. 1mg/ L = 1kg/1000 m 3 For every 1000 m 3 water of flow, we will need to use 15 kg chlorine. 15kg Cl 2 x 8500 m 3 /d = kg Cl 2 / d 1000 m 3 Above we express 15 mg/l as 15 kg Cl 2 / 1000 m 3 and multiplied it by the flow to obtain the answer expressed as kg Cl 2 / d 2. We know that 1mg/ L = 1kg/1000 m 3 We are told we use 94.8 kg chlorine for every 7900 m 3 water kg Cl 2 / d = 12kg Cl 2 = 12mg/L 7.9 x 1000 m 3 /d 1000 m 3 3. Feed Rate = W x Dosage = x Dose = 217.5kg/day We know that the chlorine dose is equal to the demand plus the residual. 2.3 mg/l mg/l = 2.8 mg/l 5. We are told in the problem that 60% of the hypochlorite is available chlorine which is the portion of the solution capable of disinfecting. Solving the equation we have: kg/d hypochlorite = 98 kg/d of chlorine needed 0.6 available chlorine in solution = kg/d hypochlorite solution 6. We are told 4 kg of chlorine will do the job of disinfection. By a 5% solution we mean that 5% by mass of the solution is to be made up of chlorine. So 100 kg of 5% hypochlorite solution will contain 5kg of chlorine. Using the formula for ratios A = C B D We substitute: 5 kg chlorine = 4kg chlorine required 100 kg solution? kg solution required Since D = C x B = 4kg x 100kg = 80 kg solution A 5 kg 7. V 1 = C 2 V 2 V 1 = (0.5mg/L) (3600L) V 1 = 40 L C 1 45mg/L 8. C 1 = C 2 V 2 C 1 = (0.02 mg/l) (5000L) C 1 = 4.9.mg/L V 1 70L

41 41 End Suction Lift Definition:

42 42 PUMPING RATES Definition: The volume of wastewater that is moved by a pump over a certain amount of time. As an example, a pump may have a pumping rate of 3L/second. It is important to understand that in many cases, you may need to convert from one set of units to another. You may be told that a pumping rate is 30L/second but will be asked to calculate how many m 3 /day that equals. 300 L 100 seconds (1 min, 40 sec) to pump tank out Pump Pumping rate is an expression of Volume Time If you know that a pump has a certain rate if discharge (pumping rate) then you can calculate things such as the amount of time it would take to fill or empty a tank or truck.

43 43 Pumping Rates: Questions 1. It takes 8 minutes to fill a tank that holds 480L of water. What is the pumping rate of the pump that is moving the water? 2. How many minutes will it take to fill a 4,800 liter truck if the pumping rate is 320 L/minute? 3. It takes an hour to fill a 3,000L tank. What is the pumping rate, expressed as L/second?

44 44 Pumping Rates: Answers 1. It takes 8 minutes to fill a tank that holds 480L of water. What is the pumping rate of the pump that is moving the water? Given: Volume = 480L Time = 8 minutes Find: Solution: Rate (ratio between these two) Q = V T = 480L 8 min = 60L 1 min Pumping rate is 60L/minute. 2. How many minutes will it take to fill a 4,800 liter truck if the pumping rate is 320 L/minute? Q = V T 320L/minute = 4800L X time (X) 320L/minute = 4800L (now divide both sides by 320) X = 4800L 320L/minute X = 15 minutes It will take 15 minutes to fill the truck if the pumping rate is 320L/minute.

45 45 3. It takes an hour to fill a 3,000L tank. What is the pumping rate, expressed as L/second? Rate = 3000L 60 minutes Rate = 3000L 3600 seconds Rate = 0.83L/second

46 46 DETENTION TIME Definition: The theoretical amount of time that a particular volume of wastewater is held for treatment in a tank or lagoon. Where Q is the flow rate V is the volume of the tank or lagoon Detention time = V Q Flow Rate Volume of tank/lagoon For example, think of detention time as the amount of time (hours, days, months, or which ever unit applies) sewage sits in a tank or lagoon, before the water is released from it. The detention time depends on the capacity of the tank/lagoon (in litres, cubic metres, etc), and the flow rate out of the tank/lagoon. Detention time can be expressed in many ways as well, depending on the units used. As an example, the detention time can vary from minutes to hours, weeks, months, or perhaps even years depending on the volume and flow rate you are dealing with.

47 47 Detention Time: Questions 1. What is the detention time (in minutes) of a 400L tank that has an outflow rate of 0.5L/second? 2. Calculate the detention time (in months) for a lagoon that holds 2,000m 3 of wastewater, and that has a discharge rate of 10m 3 /day (you can assume 30 days in an average month).

48 48 Detention Time: Answers 1. What is the detention time (in minutes) of a 400L tank that has an outflow rate of 0.5L/second? Detention time = Detention time = Volume Flow rate 400L 0.5L/sec Detention time = 800 seconds Detention time = 13 minutes, 20 seconds (approximately 13 minutes) 2. Calculate the detention time (in months) for a lagoon that holds 2,000m 3 of wastewater, and that has a discharge rate of 10m 3 /day (assume 30 days in an average month). Detention time = Volume Flow rate Detention time = 2,000m 3 10m 3 /day Detention time = Detention time = 200 days 6 months, 20 days (approximately 6 months)

49 49 WEIR OVERFLOW RATE Definition: The volume of wastewater that flows over each metre of weir length, in a given amount of time. Weir overflow rate is determined by measuring the length of the weir (outlet) and then calculating flowrate (volume per unit of time) of wastewater over the weir (outlet). It is important to be able to calculate this number. High weir overflow rates can affect the proper treatment of wastewater. Weir Overflow Rate = Flow (volume/time) Weir length (m) Lagoon Weir length (m) Flow (volume per unit of time) Weir overflow rate is often expressed as liters per second flow over each meter of weir length. For example, a weir overflow rate may be 2.5 L/s/m. In slower systems where discharge is slow and takes place over a long amount of time, weir overflow rate could be expressed as L/day/m, or m 3 /day/m, etc.

50 50 Weir Overflow Rate: Questions 1. Calculate the weir overflow rate (in liters per hour) for a system that has a weir 2.4m long, where the flow rate is 8.2L/minute. 2. If a weir is 32m long where the water flows out, calculate the weir overflow rate (in m 3 /minute) if the flow is 110 L/s.

51 51 Weir Overflow Rate: Answers 1. Calculate the weir overflow rate (in liters per hour) for a system that has a weir 2.4m long, where the flow rate is 8.2L/minute. Weir Overflow Rate = Flow (volume/time) Weir length (m) = 8.2 L/minute (now multiply 8.2 by 60 to get L/hour) 2.4 m = 492L/hour 2.4 m The weir overflow rate is 492 L/h/m. 2. If a weir is 32m long at the outflow, calculate the weir overflow rate (in m 3 /minute) if the flow is 110 L/s. Weir Overflow Rate = Flow (volume/time) Weir length (m) = 110L/second (now multiply 110 by 60 to get L/minute) 32 m = 6600L/minute (now divide 6600 by 1000 to get m 3 /minute) 32 m = 6.6 m 3 /minute (now divide 6.6 by 32 to get rate per 1m) 32 m = 0.21 m 3 /minute/m The weir overflow rate is 0.21 m 3 /min/m.

52 52 DENSITY Definition: The amount of mass that is contained in a particular volume. For example, the mass of waste compacted into a 300L trench, the mass of water in a 1 L jug, or the mass of garbage contained in a 3000 L collection truck. Density = = m V Where m is the mass V is the volume In the figure above, the box on the left has a higher density because there is more mass in the same amount of space (volume) than the box on the right. Density can be expressed in many ways, using many different units. As an example, compacted solid waste is often expressed as kilograms per cubic meter (kg/m 3 ), tons per cubic meter (tons/m 3 ), etc. You can convert back and forth using the conversion factors for volume and mass listed on the provided tables.

### Practice Tests Answer Keys

Practice Tests Answer Keys COURSE OUTLINE: Module # Name Practice Test included Module 1: Basic Math Refresher Module 2: Fractions, Decimals and Percents Module 3: Measurement Conversions Module 4: Linear,

### MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

### Section 1.7 Dimensional Analysis

Dimensional Analysis Dimensional Analysis Many times it is necessary to convert a measurement made in one unit to an equivalent measurement in another unit. Sometimes this conversion is between two units

### 1. Metric system- developed in Europe (France) in 1700's, offered as an alternative to the British or English system of measurement.

GS104 Basics Review of Math I. MATHEMATICS REVIEW A. Decimal Fractions, basics and definitions 1. Decimal Fractions - a fraction whose deonominator is 10 or some multiple of 10 such as 100, 1000, 10000,

### Unit 3.3 Metric System (System International)

Unit 3.3 Metric System (System International) How long is a yard? It depends on whom you ask and when you asked the question. Today we have a standard definition of the yard, which you can see marked on

### Lab 1: Units and Conversions

Lab 1: Units and Conversions The Metric System In order to measure the properties of matter, it is necessary to have a measuring system and within that system, it is necessary to define some standard dimensions,

### Section 1.6 Systems of Measurement

Systems of Measurement Measuring Systems of numeration alone do not provide enough information to describe all the physical characteristics of objects. With numerals, we can write down how many fish we

### APPENDIX H CONVERSION FACTORS

APPENDIX H CONVERSION FACTORS A ampere American Association of State AASHTO Highway & Transportation Officials ABS (%) Percent of Absorbed Moisture Abs. Vol. Absolute Volume ACI American Concrete Institute

### Homework 1: Exercise 1 Metric - English Conversion [based on the Chauffe & Jefferies (2007)]

MAR 110 HW 1: Exercise 1 Conversions p. 1 1-1. THE METRIC SYSTEM Homework 1: Exercise 1 Metric - English Conversion [based on the Chauffe & Jefferies (2007)] The French developed the metric system during

### MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips

MATH FOR NURSING MEASUREMENTS Written by: Joe Witkowski and Eileen Phillips Section 1: Introduction Quantities have many units, which can be used to measure them. The following table gives common units

### 4.5.1 The Metric System

4.5.1 The Metric System Learning Objective(s) 1 Describe the general relationship between the U.S. customary units and metric units of length, weight/mass, and volume. 2 Define the metric prefixes and

### Pump Formulas Imperial and SI Units

Pump Formulas Imperial and Pressure to Head H = head, ft P = pressure, psi H = head, m P = pressure, bar Mass Flow to Volumetric Flow ṁ = mass flow, lbm/h ρ = fluid density, lbm/ft 3 ṁ = mass flow, kg/h

### Mathematics For Wastewater Operators

Mathematics For Wastewater Operators Chapter 17: Mathematics The understanding of the mathematics of wastewater treatment is an important tool for all wastewater system operators. This chapter covers most

### Measurement. Customary Units of Measure

Chapter 7 Measurement There are two main systems for measuring distance, weight, and liquid capacity. The United States and parts of the former British Empire use customary, or standard, units of measure.

### BASIC MATH FORMULAS - CLASS I. A. Rectangle [clarifiers, ponds] I = length; w = width; A = area; area in square ft [sq ft]

WASTEWATER MATH CONVERSION FACTORS 1. 1 acre =43,560 sq ft 2. 1 acre =2.47 hectares 3. 1 cu ft [of water] = 7.48 gallons 4. 1 cu ft [of water] = 62.4 Ibs/ft 3 5. Diameter =radius plus radius, D =r + r

### Work, Power & Conversions

Purpose Work, Power & Conversions To introduce the metric system of measurement and review related terminology commonly encountered in exercise physiology Student Learning Objectives After completing this

### MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:

MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding

### Handout Unit Conversions (Dimensional Analysis)

Handout Unit Conversions (Dimensional Analysis) The Metric System had its beginnings back in 670 by a mathematician called Gabriel Mouton. The modern version, (since 960) is correctly called "International

### 2. List the fundamental measures and the units of measurement for each. 3. Given the appropriate information, calculate force, work and power.

Lab Activity 1 The Warm-Up Interpretations Student Learning Objectives After Completing this lab, you should be able to: 1. Define, explain and correctly use the key terms. 2. List the fundamental measures

### METRIC SYSTEM CONVERSION FACTORS

METRIC SYSTEM CONVERSION FACTORS LENGTH 1 m = 1 cm 1 m = 39.37 in 2.54 cm = 1 in 1 m = 1 mm 1 m = 1.9 yd 1 km =.621 mi 1 cm = 1 mm 1 cm =.394 in 3 ft = 1 yd 1 km = 1 m 1 cm =.328 ft 1 ft = 3.48 cm 6 1

### 2. Length, Area, and Volume

Name Date Class TEACHING RESOURCES BASIC SKILLS 2. In 1960, the scientific community decided to adopt a common system of measurement so communication among scientists would be easier. The system they agreed

### UNIT 1 MASS AND LENGTH

UNIT 1 MASS AND LENGTH Typical Units Typical units for measuring length and mass are listed below. Length Typical units for length in the Imperial system and SI are: Imperial SI inches ( ) centimetres

### 4 September 2008 MAR 110 Homework 1: Met-Eng Conversions p. 1. MAR 110 Homework 1

4 September 2008 MAR 110 Homework 1: Met-Eng Conversions p. 1 1-1. THE METRIC SYSTEM MAR 110 Homework 1 Metric - English Conversion [based on the Chauffe & Jefferies (2007)] The French developed the metric

### MATHEMATICS FOR WATER OPERATORS

MATHEMATICS FOR WATER OPERATORS Chapter 16: Mathematics The understanding of the mathematics of water hydraulics (flows, pressures, volumes, horsepower, velocities) and water treatment (detention time,

### Working Math Formulas, Units, Conversions

Working Math Formulas, Units, Conversions This presentation has been adapted from Math for Subsurface Operators given at the North Carolina Subsurface Operator School Math will be used to Determine a flow

### Abbreviations and Metric Conversion Factors

B Symbols, Abbreviations and Metric Conversion Factors Signs and Symbols + plus, or more than minus, or less than ± plus or minus Feet " nches > is greater than is greater than or equal to < is less than

### REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52

REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course.

### How do scientists measure things?

Scientific Methods Lesson How do scientists measure things? KEY TERMS mass: amount of matter in an object weight: measure of the pull of gravity on an object length: distance between two points area: measure

### HFCC Math Lab General Math Topics -1. Metric System: Shortcut Conversions of Units within the Metric System

HFCC Math Lab General Math Topics - Metric System: Shortcut Conversions of Units within the Metric System In this handout, we will work with three basic units of measure in the metric system: meter: gram:

### DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

### Metric Units. The Metric system is so simple! It is based on the number 10!

Metric Units Name The Metric system is so simple! It is based on the number 10! Below is a diagram of a section of a ruler Each numbered line represents one centimeter Each small line represents one tenth

### 1 GRAM = HOW MANY MILLIGRAMS?

1 GRAM = HOW MANY MILLIGRAMS? (1) Take the 1-gram expression and place the decimal point in the proper place. 1 gram is the same as 1.0 gram (decimal point in place) (2) Move that decimal point three places

### How do I do that unit conversion?

Name Date Period Furrey How do I do that unit conversion? There are two fundamental types of unit conversions in dimensional analysis. One is converting old units to new units with in the same system of

### Conversions in the Metric System

The metric system is a system of measuring. It is used for three basic units of measure: metres (m), litres (L) and grams (g). Measure of Example Litres (L) Volume 1 L of juice Basic Units Grams (g) Mass

### Learning Centre CONVERTING UNITS

Learning Centre CONVERTING UNITS To use this worksheet you should be comfortable with scientific notation, basic multiplication and division, moving decimal places and basic fractions. If you aren t, you

### The Metric System. J. Montvilo

The Metric System J. Montvilo 1 Measuring Systems There are two major measuring systems in use: The English System and The Metric System Which do you prefer and why? 2 Measuring Systems Assuming you prefer

### Appendix G. Units of Measure

Appendix G Units of Measure A. Measurement Magnitudes of measurements are typically given in terms of a specific unit. In surveying, the most commonly used units define quantities of length (or distance),

### FLORIDA DEPARTMENT OF ENVIRONMENTAL PROTECTION Wastewater Treatment Formulas/Conversion Table

Revised February 2014 FLORIDA DEPARTMENT OF ENVIRONMENTAL PROTECTION Wastewater Treatment Formulas/Conversion Table Measurement Conversion Measurement Conversion Measurement Conversion 12 in= 1 ft 27 cu.

### EXERCISE # 1.Metric Measurement & Scientific Notation

EXERCISE # 1.Metric Measurement & Scientific Notation Student Learning Outcomes At the completion of this exercise, students will be able to learn: 1. How to use scientific notation 2. Discuss the importance

### DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

### Conversion Table Provincial Programs

Conversion Table Provincial Programs Canadian ABC Formula/Conversion Table for Water Treatment, Distribution and Laboratory Exams Alkalinity, as mg CaC0 3 /L = Amps = Volts 0hms Area of Circle = (0.785)

### Activity Standard and Metric Measuring

Activity 1.3.1 Standard and Metric Measuring Introduction Measurements are seen and used every day. You have probably worked with measurements at home and at school. Measurements can be seen in the form

### Scientific Notation. Measurement Systems. How to Write a Number in Scientific Notation

Scientific Notation The star Proxima Centauri is 23,400,000,000,000 miles away from Earth. If we could travel in a spaceship at 5,000 miles/hour, it would take over 534,000 years to get there. Scientific

### UNIT (1) MEASUREMENTS IN CHEMISTRY

UNIT (1) MEASUREMENTS IN CHEMISTRY Measurements are part of our daily lives. We measure our weights, driving distances, and gallons of gasoline. As a health professional you might measure blood pressure,

### Activity Standard and Metric Measuring

Activity 1.3.1 Standard and Metric Measuring Introduction Measurements are seen and used every day. You have probably worked with measurements at home and at school. Measurements can be seen in the form

### Dimensional Analysis #3

Dimensional Analysis #3 Many units of measure consist of not just one unit but are actually mixed units. The most common examples of mixed units are ratios of two different units. Many are probably familiar

### SELECTED MATH PROBLEMS FOR COLLECTION AND DISTRIBUTION

SELECTED MATH PROBLEMS FOR COLLECTION AND DISTRIBUTION Sidney Innerebner, PhD, PE Principal/Owner INDIGO WATER GROUP Sidney@indigowatergroup.com 303-489-9226 For More Math Problems and the Famous PEST

### CONVERSIONS AND STATISTICS

CONVERSIONS AND STATISTICS Approximate Conversion Factors for Estimating Purposes (Compacted) Granular A, M 2.2 tonnes/m 3, 2.0 tons/yd 3 Granular B 2.1 tonnes/m 3, 1.8 tons/yd 3 3/4 Crushed Gravel (Clear)

### U Step by Step: Conversions. UMultipliersU UExample with meters:u (**Same for grams, seconds & liters and any other units!

U Step by Step: Conversions SI Units (International System of Units) Length = meters Temperature: o C = 5/9 ( o F 32) Mass = grams (really kilograms) K = o C + 273 Time = seconds Volume = liters UMultipliersU

### Dimensional Analysis is a simple method for changing from one unit of measure to another. How many yards are in 49 ft?

HFCC Math Lab NAT 05 Dimensional Analysis Dimensional Analysis is a simple method for changing from one unit of measure to another. Can you answer these questions? How many feet are in 3.5 yards? Revised

### Conversions and Dimensional Analysis

Conversions and Dimensional Analysis Conversions are needed to convert one unit of measure into another equivalent unit of measure. Ratios, sometimes called conversion facts, are fractions that denote

### ABC & C 2 EP Formula/Conversion Table for Water Treatment, Distribution, & Laboratory Exams

ABC & C EP Formula/Conversion Table for Water Treatment, Distribution, & Laboratory Exams Alkalinity, as mg CaCO 3 /L = (Titrant, ml) (Acid Normality)(50,000) Sample, ml Volts Amps = Ohms * of Circle =

### Chapter 2 Measurement and Problem Solving

Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Graph of global Temperature rise in 20 th Century. Cover page Opposite page 11. Roy Kennedy Massachusetts Bay Community

### LESSON 9 UNITS & CONVERSIONS

LESSON 9 UNITS & CONVERSIONS INTRODUCTION U.S. units of measure are used every day in many ways. In the United States, when you fill up your car with gallons of gas, drive a certain number of miles to

### Calculating Area and Volume of Ponds and Tanks

SRAC Publication No. 103 Southern Regional Aquaculture Center August 1991 Calculating Area and Volume of Ponds and Tanks Michael P. Masser and John W. Jensen* Good fish farm managers must know the area

### 2) 4.6 mi to ft A) 24,288 ft B) ft C)2024 ft D) 8096 ft. 3) 78 ft to yd A) 234 yd B) 2808 yd C)26 yd D) 8.67 yd

Review questions - test 2 MULTIPLE CHOICE. Circle the letter corresponding to the correct answer. Partial credit may be earned if correct work is shown. Use dimensional analysis to convert the quantity

### Lesson 11: Measurement and Units of Measure

LESSON 11: Units of Measure Weekly Focus: U.S. and metric Weekly Skill: conversion and application Lesson Summary: First, students will solve a problem about exercise. In Activity 1, they will practice

### YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

DETAILED SOLUTIONS AND CONCEPTS - SYSTEMS OF MEASUREMENT Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST

### Units represent agreed upon standards for the measured quantities.

Name Pd Date Chemistry Scientific Measurement Guided Inquiry Teacher s Notes Work with your group using your prior knowledge, the textbook (2.1 2.7), internet research, and class discussion to complete

### Math 98 Supplement 2 LEARNING OBJECTIVE

Dimensional Analysis 1. Convert one unit of measure to another. Math 98 Supplement 2 LEARNING OBJECTIVE Often measurements are taken using different units. In order for one measurement to be compared to

### INTERIM UNITS OF MEASURE As suggested by Federal Standard 376B January 27, 1993. hectare (ha) Hundred for traffic buttons.

SI - The Metrics International System of Units The International System of Units (SI) is a modernized version of the metric system established by international agreement. The metric system of measurement

### Sample Questions Chapter 2. Stoker

Sample Questions Chapter 2. Stoker 1. The mathematical meaning associated with the metric system prefixes centi, milli, and micro is, respectively, A) 2, 4, and 6. B) 2, 3, and 6. C) 3, 6, and 9. D) 3,

### Unit Conversions. Ben Logan Feb 10, 2005

Unit Conversions Ben Logan Feb 0, 2005 Abstract Conversion between different units of measurement is one of the first concepts covered at the start of a course in chemistry or physics.

### Sample Exercise 1.1 Distinguishing Among Elements, Compounds, and Mixtures

Sample Exercise 1.1 Distinguishing Among Elements, Compounds, and Mixtures White gold, used in jewelry, contains gold and another white metal such as palladium. Two different samples of white gold differ

### 10 g 5 g? 10 g 5 g. 10 g 5 g. scale

The International System of Units, or the SI Units Vs. Honors Chem 1 LENGTH In the SI, the base unit of length is the Meter. Prefixes identify additional units of length, based on the meter. Smaller than

### Jones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION.

Chapter 3 Metric System You shall do no unrighteousness in judgment, in measure of length, in weight, or in quantity. Just balances, just weights, shall ye have. Leviticus. Chapter 19, verse 35 36. Exhibit

### CHM 130LL: Introduction to the Metric System

CHM 130LL: Introduction to the Metric System In this experiment you will: Determine the volume of a drop of water using a graduated cylinder Determine the volume of an object by measuring its dimensions

### Measurement: Converting Distances

Measurement: Converting Distances Measuring Distances Measuring distances is done by measuring length. You may use a different system to measure length differently than other places in the world. This

### METRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281 Feet Metres 3.281 Feet Kilometres 0.

Linear Measure Square Measure or Area Volume or Capacity Mass Density Force* Pressure* or Stress* Temperature METRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281

### Section 1 Tools and Measurement

Section 1 Tools and Measurement Key Concept Scientists must select the appropriate tools to make measurements and collect data, to perform tests, and to analyze data. What You Will Learn Scientists use

### Metric Conversions Ladder Method. T. Trimpe 2008

Metric Conversions Ladder Method T. Trimpe 2008 http://sciencespot.net/ KILO 1000 Units 1 2 HECTO 100 Units Ladder Method DEKA 10 Units 3 Meters Liters Grams DECI 0.1 Unit CENTI 0.01 Unit MILLI 0.001 Unit

### PHYSICS 151 Notes for Online Lecture #1

PHYSICS 151 Notes for Online Lecture #1 Whenever we measure a quantity, that measurement is reported as a number and a unit of measurement. We say such a quantity has dimensions. Units are a necessity

### Metric Mania Conversion Practice. Basic Unit. Overhead Copy. Kilo - 1000 units. Hecto - 100 units. Deka - 10 units. Deci - 0.

Metric Mania Conversion Practice Overhead Copy Kilo - 1000 Hecto - 100 Deka - 10 To convert to a larger unit, move decimal point to the left or divide. Basic Unit Deci - 0.1 To convert to a smaller unit,

### millimeter centimeter decimeter meter dekameter hectometer kilometer 1000 (km) 100 (cm) 10 (dm) 1 (m) 0.1 (dam) 0.01 (hm) 0.

Section 2.4 Dimensional Analysis We will need to know a few equivalencies to do the problems in this section. I will give you all equivalencies from this list that you need on the test. There is no need

### Numbers and Calculations

Numbers and Calculations Topics include: Metric System, Exponential Notation, Significant Figures, and Factor-Unit Calculations Refer to Chemistry 123 Lab Manual for more information and practice. Learn

### Note that the terms scientific notation, exponential notation, powers, exponents all mean the same thing.

...1 1.1 Rationale: why use scientific notation or powers?...1 1.2 Writing very large numbers in scientific notation...1 1.3 Writing very small numbers in scientific notation...3 1.4 Practice converting

### Module 28: Basic Math

Wastewater & Drinking Water Operator Certification Training Module 28: Basic Math This course includes content developed by the Pennsylvania Department of Environmental Protection (Pa. DEP) in cooperation

### Lesson 21: Getting the Job Done Speed, Work, and Measurement Units

Lesson 2 6 Lesson 2: Getting the Job Done Speed, Work, and Measurement Student Outcomes Students use rates between measurements to convert measurement in one unit to measurement in another unit. They manipulate

### One basic concept in math is that if we multiply a number by 1, the result is equal to the original number. For example,

MA 35 Lecture - Introduction to Unit Conversions Tuesday, March 24, 205. Objectives: Introduce the concept of doing algebra on units. One basic concept in math is that if we multiply a number by, the result

### Appendix C: Conversions and Calculations

Appendix C: Conversions and Calculations Effective application of pesticides depends on many factors. One of the more important is to correctly calculate the amount of material needed. Unless you have

### FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

### Measurements. SI Units

Measurements When you measure something, you must write the number with appropriate unit. Unit is a standard quantity used to specify the measurement. Without the proper unit, the number you write is meaningless.

### Metric Conversion: Stair-Step Method

ntroduction to Conceptual Physics Metric Conversion: Stair-Step Method Kilo- 1000 Hecto- 100 Deka- 10 Base Unit grams liters meters The Metric System of measurement is based on multiples of 10. Prefixes

### .001.01.1 1 10 100 1000. milli centi deci deci hecto kilo. Explain that the same procedure is used for all metric units (meters, grams, and liters).

Week & ay Week 15 ay 1 oncept/skill ompare metric measurements. Standard 7 MG: 1.1ompare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles

### CH 304K Practice Problems

1 CH 304K Practice Problems Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. How many millimeters are there in 25 feet? a. 7.6 10 2 mm b.

### Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8. Strand: Measurement

Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8 Strand: Measurement Standards of Learning Blueprint Summary Reporting Category Grade 5 SOL Number of Items Number & Number Sense 5.1, 5.2(a-b),

### Prealgebra Textbook. Chapter 6 Odd Solutions

Prealgebra Textbook Second Edition Chapter 6 Odd Solutions Department of Mathematics College of the Redwoods 2012-2013 Copyright All parts of this prealgebra textbook are copyrighted c 2009 in the name

### Conversions. 12 in. 1 ft = 1.

Conversions There are so many units that you can use to express results that you need to become proficient at converting from one to another. Fortunately, there is an easy way to do this and it works every

### Math. The top number (numerator) represents how many parts you have and the bottom number (denominator) represents the number in the whole.

Math This chapter is intended to be an aid to the operator in solving everyday operating problems in the operation of a water system. It deals with basic math that would be required for an operator to

### Metric Conversion Factors

332 Metric Conversion Factors The following list provides the conversion relationship between U.S. customary units and SI (International System) units. The proper conversion procedure is to multiply the

### Pacific Pump and Power

Pacific Pump and Power 91-503 Nukuawa Street Kapolei, Hawaii 96707 Phone: (808) 672-8198 or (800) 975-5112 Fax: (866) 424-0953 Email: sales@pacificpumpandpower.com Web: www.pacificpumpandpower.com Table

### Measurement/Volume and Surface Area Long-Term Memory Review Grade 7, Standard 3.0 Review 1

Review 1 1. Explain how to convert from a larger unit of measurement to a smaller unit of measurement. Include what operation(s) would be used to make the conversion. 2. What basic metric unit would be

### TIME ESTIMATE FOR THIS LESSON One class period

TITLE OF LESSON Physical Science Unit 1 Lesson 2 Systéme Internationale aka the Metric System Nature of Matter: How do tribes standardize their lives? TIME ESTIMATE FOR THIS LESSON One class period ALIGNMENT

### Measure the Lakes SOURCES CONSULTED

K. Kelly Mottl kamottl@gbaps.org Washington Middle School, Green Bay, WI Measure the Lakes LESSON OVERVIEW Measuring the Lakes by K. Kelly Mottl has been designed to help students use mathematics, the

### Converting Units of Measure Measurement

Converting Units of Measure Measurement Outcome (lesson objective) Given a unit of measurement, students will be able to convert it to other units of measurement and will be able to use it to solve contextual

### Measurements 1. BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com. In this section we will look at. Helping you practice. Online Quizzes and Videos

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Measurements 1 In this section we will look at - Examples of everyday measurement - Some units we use to take measurements - Symbols for units and converting

### CONNECT: Currency, Conversions, Rates

CONNECT: Currency, Conversions, Rates CHANGING FROM ONE TO THE OTHER Money! Finances! \$ We want to be able to calculate how much we are going to get for our Australian dollars (AUD) when we go overseas,

### A Mathematical Toolkit. Introduction: Chapter 2. Objectives

A Mathematical Toolkit 1 About Science Mathematics The Language of Science When the ideas of science are epressed in mathematical terms, they are unambiguous. The equations of science provide compact epressions